Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Recently in, a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F4 for number of transmit antennas N = 2m, m >; 1, and rates R >; 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N, R) pairs. The new full-rate codes of this paper (R = N) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over F4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations.

Quantum Error Correction via Codes over GF(2)

It is well known that n-length stabilizer quantum error correcting codes (QECCs) can be obtained via n-length classical error correction codes (CECCs) over GF(4), that are additive and self-orthogonal with respect to the trace Hermitian inner product. But, most of the CECCs have been studied with respect to the Euclidean inner product. In this paper, it is shown that n-length stabilizer QECCs can be constructed via 371 length linear CECCs over GF(2) that are self-orthogonal with respect to the Euclidean inner product. This facilitates usage of the widely studied self-orthogonal CECCs to construct stabilizer QECCs. Moreover, classical, binary, self-orthogonal cyclic codes have been used to obtain stabilizer QECCs with guaranteed quantum error correcting capability. This is facilitated by the fact that (i) self-orthogonal, binary cyclic codes are easily identified using transform approach and (ii) for such codes lower bounds on the minimum Hamming distance are known. Several explicit codes are constructed including two pure MDS QECCs.

Prediction of load-deflection behaviour using fracture energy GF: A comparative study of two fracture models for concrete

Load-deflection curves for a notched beam under three-point load are determined using the Fictitious Crack Model (FCM) and Blunt Crack Model (BCM). Two values of fracture energy GF are used in this analysis: (i) GF obtained from the size effect law and (ii) GF obtained independently of the size effect. The predicted load-deflection diagrams are compared with the experimental ones obtained for the beams tested by Jenq and Shah. In addition, the values of maximum load (Pmax) obtained by the analyses are compared with the experimental ones for beams tested by Jenq and Shah and by Bažant and Pfeiffer. The results indicate that the descending portion of the load-deflection curve is very sensitive to the GF value used.

Fast-Group-Decodable STBCs via Codes over GF(4)

In this paper we construct low decoding complexity STBCs by using the Pauli matrices as linear dispersion matrices. In this case the Hurwitz-Radon orthogonality condition is shown to be easily checked by transferring the problem to $\mathbb{F}_4$ domain. The problem of constructing low decoding complexity STBCs is shown to be equivalent to finding certain codes over $\mathbb{F}_4$. It is shown that almost all known low complexity STBCs can be obtained by this approach. New codes are given that have the least known decoding complexity in particular ranges of rate.

Synthesis and properties of main chain discotic liquid crystalline polyethers based on rufigallol

Two series of thermotropic main chain discotic liquid crystalline polyethers, PR4m-n, based on rufigallol were prepared starting from the symmetric tetraethers of rufigallol, R4m; m and n represent the number of carbon atoms in the side chain and spacer segment, respectively. The symmetric tetraethers were in turn readily prepared by selective alkylation of rufigallol under controlled phase-transfer conditions. GPC analysis of the polymers suggested that they were all of moderate molecular weights, with M-n varying between 5400 and 17 000. The length of the spacer segment n in these polyethers was systematically varied, and its effect on the phase transition temperatures and the mesophase structure was examined using DSC, polarized light microscopy, and X-ray diffraction. It is noticed that when the spacer lengths are relatively long(n greater than or equal to 2m), the isotropization temperature (TD-i) decreases as the spacer length n increases, an observation that is in accordance with those previously made. However, when the spacer lengths are relatively small (n < 2m), the dependence of TD-i is quite the opposite; TD-i actually increases with an increase in spacer length. Furthermore, X-ray diffraction studies indicate that, in the discotic columnar mesophases that are formed, the columns pack in a hexagonal manner when n greater than or equal to 2m, while they do so in a rectangular lattice when n < 2m, leading to the formation of Dh and Dr mesophases, respectively. Finally, comparison of the discotic polyethers with their low molar mass analogues confirms the role of polymerization in stabilizing the mesophase; while all the polymers exhibit columnar mesophases, some of their low molar mass analogues are not liquid crystalline.

Space and time efficiency of the forest-of-quadtrees representation

A forest of quadtrees is a refinement of a quadtree data structure that is used to represent planar regions. A forest of quadtrees provides space savings over regular quadtrees by concentrating vital information. The paper presents some of the properties of a forest of quadtrees and studies the storage requirements for the case in which a single 2m × 2m region is equally likely to occur in any position within a 2n × 2n image. Space and time efficiency are investigated for the forest-of-quadtrees representation as compared with the quadtree representation for various cases.

Determination of the magnetic moment by QCD sum rules

The magnetic moment of the Λ hyperon is calculated using the QCD sum-rule approach of Ioffe and Smilga. It is shown that μΛ has the structure μΛ=(2/3(eu+ed+4es)(eħ/2MΛc)(1+δΛ), where δΛ is small. In deriving the sum rules special attention is paid to the strange-quark mass-dependent terms and to several additional terms not considered in earlier works. These terms are now appropriately incorporated. The sum rule is analyzed using the ratio method. Using the external-field-induced susceptibilities determined earlier, we find that the calculated value of μΛ is in agreement with experiment.

Purification of a bacterial organophosphate-hydrolysing phosphatase by cibacron 3GA-Sepharose affinity chromatography

A phosphatase catalysing the hydrolysis of organophosphorus pesticides was purified to homogeneity using Cibacron 3GA-Sepharose CL 6B affinity chromatography. The enzyme which is localized in the periplasm of the bacterium Image NC5 was extracted by treating with 0.2M MgCl2, pH 8.4. The enzyme was adsorbed to the Cibacron-Sepharose at pH 7.0 and eluted with Tris-HCl buffer at pH 8.0, with 47 per cent recovery. The enzyme thus obtained was electrophoretically homogeneous. This simple affinity purification procedure enhances the potential for its use in large scale detoxification systems.

Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

High Resoulution Electron Microscopy of Chloritoid Minerals From Different Geological Melieu

Structural defects of three chloritoid minerals from distinet geologic melieu have been investigated by high resolution electron microscopy. X-ray powder and electron diffraction patterns indicate that the chloritoid from one geological source (A) is2M 1+2M2 monoclinic variant while those from another geological source (B) are 2M 2 monoclinic variants. In a typical one-dimensional lattice image of a crystal from sourceA, the 2M 2 matrix is broken by insertion of triclinic inter-growths. Another crystal with the 2M 2 matrix showed single, triple, quadruple and quintuple layers displaying an unusually high degree of disorder. Lattice images of 2M 2 monoclinic variants from sourceB yielded more homogeneous micrographs. The important finding from the present studies is that the chloritoid from sourceA is a severely disordered low-temperature intermediate phase in the conversion of the triclinic chloritoid to the high-temperature ordered monoclinic variants of sourceB. Severely disordered chloritoids, marking the beginning of low grade metamorphism, are generated as intermediates between the state of complete disordered arrangement towards the end of low grade metamorphism within the narrow stability range of 400°–500°C.

Thermal analysis of metal sulfate hydrazinates and hydrazinium metal sulfates

Thermal analysis of metal sulfate hydrazinates, MSO4·xN2H4 (I) (M=Mn, Co, Ni, Zn, Cd; x = 2–3), hydrazinium metal sulfates, (N2H5)2M(SO4)2 (II) (M=Mn, Cu, Zn, Cd), and N2H5LiSO4 have been studied using simultaneous TG-DTGDTA. Both types of complexes, I and II, decompose to the respective metal sulfates or a mixture of metal sulfide and sulfate.

Thermal decomposition of hydrazinium aluminium sulfate hydrate and hydrazinate

As a part of our research programme on hydrazine derivatives [I-4]. we have prepared a number of hydrazinium metal sulfates [ 1.S] (N2 H5), M(SO4)2, where M = Mn, Fe, Co, Ni, Cu. Zn, Cd and Mg and their hydrazine adducts [2] of the type (N2H5)2M(SO4)2 . 3 N2H4. where M = Fe, Co and Ni, as well as N2H5AI(SO4)2 . 6N2H4. Recently, we reported [5.6] the thermal analysis of these compounds. Our .literature survey on the thermal analysis of alums [7] and aluminium salts [8] indicated that, although the preparation of hydrazinium aluminium sulfate dodecahydrate, N2H5Al(SO4)2 . 12 H2O, has been reported [9], there appears to be no report on its thermal analysis. Here, we report the results df the thermal analysis of N2H5Al(SO4)2 . 12 H2O and N2H5Al(SO4)2 . 2N2H4.

Transport of retinol in the duck plasma

Retinol-binding protein and prealbumin were isolated from duck plasma by chromatography on DEAE-cellulose-and DEAE-Sephadex A-50, gel filtration on Sephadex G- 100 and preparative Polyacrylamide gel electrophoresis. The molecular weights of the retinolbinding protein-prealbumin complex, prealbumin and retinol-binding protein were found to be 75,000, 55,0000 and 20,000, respectively. On sodium dodecyl sulphate Polyacrylamide gel electrophoresis, prealbumin dissociated into identical subunits exhibiting a molecular weight of 13,500. Retinol-binding protein exhibited microheterogeneity on electrophoresis, whereas prealbumin moved as a single band unlike the multiple bands observed in chicken and rat.The ultraviolet and fluorescence spectra of the two proteins were similar to those isolated from other species. No carbohydrate moiety was detected in either retinol-binding protein or prealbumin. Duck retinol-binding protein and prealbumin showed cross-reactivity with their counterparts in chicken but differed immunologically from those of goat and man. Retinolbinding protein and prealbumin could be dissociated at low ionic strength, in 2M urea, by CMsephadex chromatography or on preparative electrophoresis. Although the transport of retinol in duck plasma is mediated by carrier proteins as in other species, it is distinguished by the absence of microheterogeneity in prealbumin and of an apo-retinol-binding protein form that could be transported in the plasma.

Equivalent rate 1/2 quasi-cyclic codes

Chen et al. [1] give a list of quasi-cyclic (2m,m) codes which have the largest minimum distance of any quasi-cyclic code, for various values ofm. We present the weight distribution of these codes. It will be seen that many of the codes found by Chen et al. [1] are equivalent in the sense of having identical weight distributions.